(a) The "average value" of a function over an interval [a,b] is defined to be
(1/(b-a)) times the integral of f from the limits x= a to x = b.
Now S = 200(5 - 9/(2+t))
The average value of S during the first year (from t = 0 months to t = 12 months) is then:
(1/12) times the integral of 200(5 - 9/(2+t)) from t = 0 to t = 12
or 200/12 times the integral of (5 - 9/(2+t)) from t= 0 to t = 12
This equals 200/12 * (5t -9ln(2+t))
Evaluating this with the limits t= 0 to t = 12 gives:
708.113 units., which is the average value of S(t) during the first year.
(b). We need to find S'(t), and then equate this with the average value.
Now S'(t) = 1800/(t+2)^2
So you're left with solving 1800/(t+2)^2 = 708.113
<span>I'll leave that to you</span>
The volume of the original cylinder is
... V = π·r²·h
For r=1 and h=1, this is
... V = π·1²·1 = π
For the new cylinder, the volume is 1.089 times that amount.
... V = 1.089π = π·1.1²·(1-k)
... 1.089/1.21 = 1-k
... k = 1 - 1.089/1.21 = 1 - 0.9 = 0.1 = 10%
The appropriate choice is (B) 10.
Answer:
1.) He still owes $100 of debt
2.) 1 rose would be .75 cents and 1 carnation would be .90 cents
3.) C 8 and 3/8
Step by Step explanation
(/ means divided by in the first 2 equations but / in the last question is for the fractions.)
1.) _(1,500 / 3 =500. 1,500 - 500 =1,000 / 5 =200 x 3 =600. 700 - 600 =$100)
2.)_(1.50/2 =.75 cents. 2.70/3 =.90 cents.)
3.) i first added the fractions ( i equalized them) then i added the whole numbers (the u in the equation was to separate the whole num. and fraction )
Before i equalized it: (6u3/4 + 1u1/8 = 7u1/8 + 1/8 = 8u3/8)
After i equalized it: (6u6/8 + 1u1/8 = 7u1/8 + 1/8 = 8u3/8)
Answer:
<h2>62.8 ft</h2>
Step-by-step explanation:
